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A person gets on a Ferris wheel at the starting point. The starting point is 15 feet off the ground. The Ferris wheel has a radius of 50 feet. What is the height of the rider from the ground after the Ferris wheel rotates 11π/12 radians?

A person gets on a Ferris wheel at the starting point The starting point is 15 feet off the ground The Ferris wheel has a radius of 50 feet What is the height o class=

Respuesta :

danielmaduroh

Answer:

[tex]\boxed{\frac{25}{2}(\sqrt{6}+\sqrt{2})+65}[/tex]

Explanation:

The height of the rider from the ground after the Ferris wheel equals the starting point is 15 feet off the ground plus the radius of the Ferris wheel plus the opposite side of the triangle ΔABC (See figure below). Hence our goal is to find this side. We have the angle [tex]11\pi /2=165^{\circ}[/tex], therefore the angle ∠BAC = 165° - 90° = 75°. So this side can be found using trigonometry:

[tex]\overline{BC}=\overline{AB}sin(75^{\circ})=50sin(75^{\circ})=\frac{25}{2}(\sqrt{6}+\sqrt{2})[/tex]

Finally, the height is:

[tex]H=\frac{25}{2}(\sqrt{6}+\sqrt{2})+15+50 \\ \\ \boxed{H=\frac{25}{2}(\sqrt{6}+\sqrt{2})+65}[/tex]

Ver imagen danielmaduroh
ashishdwivedilVT

The height of the rider from the ground after the Ferris wheel rotates 11π/12 radians is 65 + [tex]\frac{25}{2} (\sqrt{6} +\sqrt{2} )[/tex].

It is given that

The radius of the Ferris wheel = 50feet

Angle θ will be  11π/12-π/2 = 5π/12 =75°

What is the sine of an angle?

The sine of an angle is the ratio of the opposite side to the hypotenuse.

From the diagram attached,

sinθ = [tex]\frac{h}{50}[/tex]

sin 75 = h/50

h = 50*sin75

h = 50sin(45+30)

h = [tex]\frac{25}{2} (\sqrt{6} +\sqrt{2} )[/tex]

so, the height of the rider from the ground after the Ferris wheel rotates 11π/12 radians = 15+50+h = 65 + [tex]\frac{25}{2} (\sqrt{6} +\sqrt{2} )[/tex].

Therefore, the height of the rider from the ground after the Ferris wheel rotates 11π/12 radians is 65 + [tex]\frac{25}{2} (\sqrt{6} +\sqrt{2} )[/tex].

To get more about trigonometric ratios visit:

https://brainly.com/question/24349828

Ver imagen ashishdwivedilVT

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